Characterizations of Spatial Quaternionic Partner-Ruled Surfaces

Abstract

In this paper, we investigate the spatial quaternionic expressions of partner-ruled surfaces. Moreover, we formulate the striction curves and dralls of these surfaces by use of the quaternionic product. Furthermore, the pitches and angles of pitches are interpreted for the spatial quaternionic ruled surfaces that are closed. Additionally, we calculate the integral invariants of these surfaces using quaternionic formulas. Finally, the partner-ruled surfaces of a given spatial quaternionic ruled surface are demonstrated as an example, and their graphics are drawn.

Keywords

• spatial quaternion
• quaternionic curve
• partner-ruled surface
• striction curves
• pitches and angle of pitches